The main objective of the proposed research is to develop the mathematical analysis of the steady state equations for networks of flow tubes that represet te complete multinephron model of the mammalian kidney. These problems consists of complicated systems of nonlinear differential equations along with boundary conditions determined by the geometry of the flow tubes. The analysis will include existence criteria, uniqueness - nonuniquesness studies, bounds for solutions, and stability studies for these boundary value problems. Results of this type, some of which are due to the proposed investigator, have been recently given for systems of flow tubes. For the general problem, these results do not allow variable pressures in the tubes and active transport between the tubes and, thus, do not apply to a complete model of the kidney. The proposed research project will attempt to fill gaps in these results and to extend the results to models that include complete nephrons of the kidney. Methods to be used include fixed point arguments, applicaions of the implicit function theorem, matching known solutions of simplified problems to yield solutions of the general problem, and analysis, including numerical work, or reduced perturbation problems.